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  • 1
    Electronic Resource
    Electronic Resource
    A small angle x-ray scattering study of the droplet–cylinder transition in oil-rich sodium bis(2-ethylhexyl) sulfosuccinate microemulsions (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 1651-1665 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A method for nonlinear fitting of x-ray scattering data from polydisperse mixtures was developed. It was applied to the analysis of the structural changes in the droplet phase of oil-rich water-in-oil (w/o) sodium bis(2-ethylhexyl) sulfosuccinate (AOT) microemulsions with increasing temperature or upon addition of salt. Data were collected at different temperatures (15 to 60 °C) and salt concentrations (up to 0.6% NaCl) within the one-phase region of the L2 phase (w/o microemulsion) for different droplet sizes (water/AOT molar ratio wo=25 to 56) and concentrations (droplet weight fraction cw=2% to 20%). This allowed us to distinguish between contributions from individual scattering particles, e.g., droplets and cylinders to the total scattering intensity. The complete data set containing over 500 scattering curves could be interpreted by fitting the scattering of weighted sums of AOT covered water droplets, long cylinders, and inverse AOT micelles containing bound water only, to the experimental scattering curves. The polydispersity of the droplets and cylinders is described by Schulz distributions and the interactions between the droplets are calculated using a sticky hard-sphere potential in the Percus–Yevick approximation. The volume fractions of the components, their average sizes and polydispersity, and the stickiness of the water/AOT droplets are determined by a nonlinear fit to the experimental data. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481954
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  • 2
    Electronic Resource
    Electronic Resource
    Small-angle-scattering-data treatment by the regularization method (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 244-250 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The application of Tikhonov's regularization method [Tikhonov & Arsenin (1977). Solution of Ill-Posed Problems. New York: Wiley] for the solution of ill-posed problems in small-angle-scattering-data treatment is considered. Simple regularization algorithms are proposed for solving convolution equations in data desmearing (slit-width and polychromaticity problems) as well as for polydispersity problems. A general indirect approach of data processing based on the regularization method is described. Comparison with other data-treatment methods is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387011255
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  • 3
    Electronic Resource
    Electronic Resource
    A weighted rotation function (1997)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 53 (1997), S. 789-791 
    Details
    ISSN: 1399-0047
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple probability expression is derived to discriminate the intermolecular vectors in the cross rotation function. The radial weighting function introduced takes into account both particle anisometry and crystal packing and can be incorporated into existing molecular replacement packages.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0907444997006197
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  • 4
    Electronic Resource
    Electronic Resource
    Small-angle scattering: direct structure analysis (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 827-835 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract A direct method for structural interpretation of small-angle scattering data by monodisperse isotropic systems is presented. The spherical harmonics technique proposed by Stuhrmann [Acta Cryst. (1970), A26, 297-306] is used to choose the class of possible solutions. The method enables one to decompose scattering intensity into partial amplitudes corresponding to different multipole components of scattering density using the space and value density restrictions. If a particle possesses a rotational symmetry, its structure may be restored directly using the method; if not, additional information is required to get a set of possible solutions. The method is stable with respect to experimental errors. The efficiency of the procedure is shown in model examples. The application of the method to interpret the small-angle X-ray scattering curve of bacteriophage T7 produced a map of electron density with a resolution of about 12 Å.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482001703
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  • 5
    Electronic Resource
    Electronic Resource
    The solution of the one-dimensional sign problem for Fourier transforms (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 137-142 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An iterative procedure for the determination of the signs of scattering amplitudes is considered. It is assumed that the scattering density is a one-dimensional antisymmetric function with a limited range of definition. The convergence of the method to a rigorous solution is proved. The stability of the procedure with respect to various experimental errors is shown in model examples. The proof can be generalized for a one-dimensional phase determination of a continuous intensity distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384000301
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  • 6
    Electronic Resource
    Electronic Resource
    Size distributions of metal nanoparticles in polyelectrolyte gels (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 11109-11116 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Small-angle x-ray scattering is used to study size distributions of noble metal nanoparticles embedded in polyelectrolyte hydrogels with oppositely charged surfactants. A procedure is proposed to subtract matrix scattering and to extract pure scattering due to the nanoparticles allowing to evaluate their size distribution functions by means of a regularization technique. Two kinds of collapsed gel-surfactant complexes were studied: a complex of a cationic gel of poly(diallyldimethylammonium chloride) with an anionic surfactant sodium dodecyl sulfate (PDADMACl/SDS), and that of an anionic gel of poly(methacrylic acid) with a cationic surfactant cetylpyridinium chloride (PMA/CPC). Addition of a gold compound (HAuCl4⋅3H2O) to the PDADMACl/SDS system forms the metal compound clusters and leads to a partial distortion of the gel structure. After subsequent reduction of the gold compound with sodium borohydride (NaBH4) ordering in the gel disappears and gold nanoparticles are formed. Their size distribution includes a fraction of small particles with approximately the same size as the compound clusters before reduction and a fraction of larger particles with the radii up to 40 nm. For the collapsed PDADMACl/SDS gels, aging does not change the size distribution profile; for the noncollapsed PDADMACl gels without surfactant, metal particles are found to grow with time. This suggests that the aggregation of metal colloids is prevented by the ordering in the collapsed gel-surfactant complex. The addition of HAuCl4⋅3H2O and the subsequent reduction of the metal ions in the PMA/CPC system does not distort the gel structure as the degree of incorporation of AuCl4− ions is very low. Particle sizes in the PMA/CPC system are found to be somewhat larger than those in the PDADMACl/SDS system. The PDADMACl/SDS gels loaded with the PtCl4 compound were also studied to analyze the influence of the reducing agent type on the particle size distribution distributions. Fast reduction with NaBH4 yielded mostly small particles with the radii around 2 nm grown from the compound clusters similar to those observed for the gold-loaded gels. In contrast, slow reduction with N2H4⋅H2O was found to produce larger nanoparticles and the size distribution function shows a major fraction of the particles with the radii up to 30 nm. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477749
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  • 7
    Electronic Resource
    Electronic Resource
    MASSHA – a graphics system for rigid-body modelling of macromolecular complexes against solution scattering data (2001)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 34 (2001), S. 527-532 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A program, MASSHA, for three-dimensional rendering and rigid-body refinement is presented. The program allows display and manipulation of high-resolution atomic structures and low-resolution models represented as smooth envelopes or ensembles of beads. MASSHA is coupled with a computational module to align structural models of different nature and resolution automatically. The main feature is the possibility for rigid-body refinement of the quaternary structure of macromolecular complexes. If high- or low-resolution models of individual subunits are available, the complex can be constructed on the computer display and refined to fit the experimental solution scattering data. MASSHA provides both interactive and automated refinement modes to position subunits in a heterodimeric complex (general case) and in a homodimeric complex with a twofold symmetry axis. Examples of application of the program (running on IBM PC compatible machines under Windows 9x/NT/2000) are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889801006100
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  • 8
    Electronic Resource
    Electronic Resource
    Determination of the regularization parameter in indirect-transform methods using perceptual criteria (1992)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 25 (1992), S. 495-503 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A method is proposed for the determination of the optimum value of the regularization parameter (Lagrange multiplier) when applying indirect transform techniques in small-angle scattering data analysis. The method is based on perceptual criteria of what is the best solution. A set of simple criteria is used to construct a total estimate describing the quality of the solution. Maximization of the total estimate is straightforward. Model computations show the effectiveness of the technique. The method is implemented in the program GNOM [Svergun, Semenyuk & Feigin (1988). Acta Cryst. A44, 244–250].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889892001663
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  • 9
    Electronic Resource
    Electronic Resource
    Restoring Three-Dimensional Structure of Biopolymers from Solution Scattering (1997)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 30 (1997), S. 792-797 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The methods of small-angle scattering data analysis, developed to study the three-dimensional structure of biological macromolecules in solution, are reviewed. The direct methods include low-resolution shape determination in the homogeneous approximation and multiphase structure search by simultaneous fitting of the contrast-variation data sets from multicomponent particles. Approaches using crystallographic data involve evaluation of the solution scattering from the atomic coordinates, taking into account the solvation shell and relative positioning of subunits (domains) with known structure in complex particles. Practical applications of these methods to study biological macromolecules in solution are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889897001039
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  • 10
    Electronic Resource
    Electronic Resource
    Shape Determination from Solution Scattering of Biopolymers (1997)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 30 (1997), S. 798-802 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Practical aspects of low-resolution shape determination in small-angle scattering studies of biological macromolecules in solution are considered. The shape restoration method using spherical harmonics [Svergun, Volkov, Kozin & Stuhrmann (1996). Acta Cryst. A52, 419–426] is extended to account for deviations from the idealized model and to work directly on raw experimental data sets. An algorithm to restore the structure of homodimeric particles in terms of the shape of the monomer and the separation between the monomers is implemented. Applications of the program to the shape restoration of several proteins, with known and unknown crystal structures, from X-ray solution-scattering data are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889897001714
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